Question

can any body tell me whats the difference between one to one function and one one correspondence??

Answer 1

a ono-to-one function is an injective function. i.e., a function that satisfies
\[ \large a\neq b\qquad\Rightarrow\qquad f(a)\neq f(b) \]

a ono-to-one correspondence is a function \(f:A\to B\) that is bijective; i.e., it is injective and surjective
\[ \large (\forall b\in B)(\exists a\in A)(b=f(a)) \]

Answer 2

we should probably specify that there exists a unique \(a\)

Answer 3

that is given by injectivity

Answer 4

it is not given by \[\large (\forall b\in B)(\exists a\in A)(b=f(a))\]